In theory, Chemical Reaction Networks (CRNs), like sufficiently elaborate
neural networks, can approximate any computable function [1]}, [2]} and therefore can
perform inference. For instance, [1]} showed how to implement
McCulloch-Pitts neurons, and thus arbitrary Boolean circuits, in
CRNs. Probabilistic computation with CRNs has also been explored:
[4]} showed how to construct a chemical reaction network whose
steady-state encodes the marginals of joint probability distributions
in a class of probabilistic models known as factor graphs. As
[4]} point out, enzyme-free DNA strand displacement
[6]} can serve as the
physical basis of such CRNs. However,
while CRNs can encode these probabilistic computations, only a
subset of CRNs can be plausibly instantiated using
cellular signaling (and the nucleic acids-based implementation of CRNs
[6]} is arguably not a
plausible intracellular mechanism). Also, the reliance on
steady-states does not capture many of the complexities of a cellular context. A cell
responds to perturbations from its environment in real-time, and does so
in the presence of considerable stochastic fluctuations in gene expression
[8]}, [9]} (such
fluctuations are not taken into account in the steady-state framework of
[4]}). This raises the question of
what biochemical circuits could theoretically realize inference in the
dynamic and stochastic environment in which cells live.
